(Yes. Low-discrepancy sequences are the WP link for "a special random number generator" in /unsort, and I considered that link to also cover quasi-Monte Carlo etc. I'm not immediately sure what you mean by "φ in a circular space" though.)
If you can arrange your space from 0,..1 and identify 1 with 0 to make it circular, obviously (consider 1/3, 2/3, etc.) advancing by any amount in ℚ will fail to explore a lot of the space. The flip side of this is that φ, or 1/φ, are the least-ℚ-like regular things in ℝ: if we consider good approximations to be places in the continued fraction where there's a large entry, that never occurs. (their continued fraction representation is repeated 1's)
This comes up with "how do sunflowers know about φ?", the answer to which seems to be: they don't, they're just creating new seeds in the least-correlated place to all the existing seeds, and because of the property above, that tends to result in apparently-spiraling placements which can be fitted with fibonaccis or φs.
Does that make sense?
(Father of the regrettably more famous Chazelle, if you’re okay californicating rabbit holes)
Now that I've pushed BC back to the stack, here's a ref that might be worthier of the (nonnewtonian) process heap
(Pls use the usual Chinese bulk carrier resilient doi tricks as might be required)
Lagniappe:
https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...
* http://bitsnbobstones.watershipdown.org/lapine/unit12.html#:...
If the constant factors aren't intolerable, it seems like one really ought to be able to do something with the fact that corruption (galois connection connexion?) only happens in one direction (corruption monad as closure)...
Lagniappe: https://www.youtube.com/watch?v=_yExwkQYcp0
(thanks for reminding me of "Have not I the most reason to complain, when I see these very Yahoos carried by Houyhnhnms in a vehicle, as if they were brutes, and those the rational creatures?"!)